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edu:topics:complex:start [2017/11/10 15:16]
simon
edu:topics:complex:start [2018/02/21 23:51] (current)
simon [notes]
Line 163: Line 163:
 √ −1, instead of being √ −1, instead of being
 called positive, negative and imaginary (or worse still, impossible) unity, been given the names say,of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity. called positive, negative and imaginary (or worse still, impossible) unity, been given the names say,of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity.
 +</​quote></​quote>​
 +
 +----
 +just like calculus was re-defined in terms of limits to eliminate "​impossible"​ infinities, so
 +complex numbers are redefined considering groups and sets ... but this requires a great deal more theory: ​
 +<​quote></​quote>​http://​www.math.uri.edu/​~merino/​spring06/​mth562/​ShortHistoryComplexNumbers2006.pdf<​quote>​
 +Augustin-Louis Cauchy (1789-1857) initiated complex function theory in an 1814 memoir
 +submitted to the French Acad´emie des Sciences. The term analytic function was not
 +mentioned in his memoir, but the concept is there. The memoir was published in 1825.
 +Contour integrals appear in the memoir, but this is not a first, apparently Poisson had
 +a 1820 paper with a path not on the real line. Cauchy constructed the set of complex
 +numbers in 1847 as R[x]/(x2 + 1)
 +<​quote>​We completely repudiate the symbol √
 +−1, abandoning it without regret because
 +we do not know what this alleged symbolism signifies nor what meaning
 +to give to it.
 </​quote></​quote>​ </​quote></​quote>​
  
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 ====notes==== ====notes====
-[[edu:​resources:​schrodinger-life]] | [[edu:​resources:​gleick-chaos]] | galileo |+[[books:​schrodinger]] | [[edu:​resources:​gleick-chaos]] | galileo |
 copernicus | [[edu:​resources:​penrose-physics]] copernicus | [[edu:​resources:​penrose-physics]]
  
edu/topics/complex/start.1510287379.txt.gz · Last modified: 2017/11/10 15:16 by simon